Determinants of the time varying
Discussion Paper No. 07/597
Department of Economics
University of Bristol
8 Woodland Road
Bristol BS8 1TN
Determinants of the time varying risk premia
University of Bristol
March 13, 2007
This paper generates monthly risk premia data using zero coupon gov-ernment treasury bills for 43 countries over the period of 1994-2006. The measure of risk premia is based on the ARCH-in-Mean (ARCH-M) model introduced by Engle, Lilien and Robins (1987). We show that the risk pre-mia are time varying and also vary considerably across sample countries. Countries with better …nancial development and higher income generally have lower risk premia of government assets. This study also examines the macroeconomic and political determinants of the risk premia by using cross-section and dynamic panel regression analyses. The results show that the risk premia are signi…cantly a¤ected by macroeconomic circum-stances, especially economic growth and the real e¤ective exchange rate. The results are robust across the majority of countries in our study.
¤The author would like to thank Andrew Pickering for his excellent supervision and
Jonathan Temple for his advice on panel regression methodologies. This paper has also been inspired from the internship project “Determinants of Term Structures (yield curve): An Empirical Analysis of East Asian Local Currency Bond Markets”, during Sept.-Dec. 2005 at the Asian Development Bank, Manila, Philippines. The usual disclaimer applies. Email: P.Chantapacdepong@bristol.ac.uk.
This paper studies the behavior of the risk premia of short term government as-sets (treasury bills). The paper makes 2 contributions to the literature. Firstly, we generate monthly risk premia data using zero coupon government treasury bills for 43 countries over the period of 1994-2006. The risk premia measure is based on the ARCH-in-Mean (ARCH-M) model introduced by Engle, Lilien and Robins (1987). The estimation of the risk premia in this paper can perform the same function as the agencies’ credit ratings as it allows us to extract the market perceptions of the risk in holding government assets. Moreover, the risk premia data generated in this study are somewhat more continuous and more time varying measure of risk in holding government asset than the risk indices based on credit ratings. We …nd that the risk premia are time varying and also vary considerably across countries. The second contribution of this paper is that we examine the macroeconomic and political determinants of the risk premia by using cross section and dynamic panel regression analyses. The results show that the risk premia are signi…cantly a¤ected by macroeconomic circumstances, especially economic growth and the real e¤ective exchange rate. The results are robust across the majority of countries in our study.
The risk premia series in this study are proxied by the time series volatility of the excess holding yields for short- and long-term treasury bills. Thus the risk premia in this study correspond to the term premia in the theory of the term structure of interest rates, I will use these two terms interchangeably. The process used to construct risk premia data follows the argument of Engle, Lilien and Robins (1987), and associates the mean of the excess returns on holding long-term comparing to short-term government bills to the volatility of the excess returns. It focuses on the fundamental trade-o¤ between expected returns and their volatility. The theoretical appeal of this model is that it
provides microeconomics foundations by measuring the response of risk averse economic agents to uncertainty using the time series data. Estimating the risk premia from the treasury bills data is relevant to previous studies which have documented that the treasury bills rates contain time varying term premia1.
There is an abundance of work on the term structure of interest rate but this focuses mainly on the validity of the expectations hypothesis. Empirical evidence of time varying risk premia in government asset returns is frequently interpreted as evidence against the expectations hypothesis. However, we need a better understanding of the determinants of the term premia. This will in turn give clearer explanation for the rejection of expectations hypothesis.
The literature has not yet fully identi…ed the determinants of risk premia in government assets. There are a few works that attempt to relate the term struc-ture to movements in macroeconomic variables such as Wu (2002), Hordahl, Tristani, and Vestin (2003), and Rudebusch and Wu (2003). However, these works ignore the role of time-varying risk premia which is an important com-ponent in explaining movements in yields over time. Ang and Piazzesi (2003) suggest that macroeconomic factors (in‡ation and economic growth factors) have an important explanatory role for the dynamics of the yield curve, and that including these variables in a term structure model can improve its one-step ahead forecasting performance2. They …nd that macro factors explain up
to 85% of the observed variation in bond yields. Hordahl, Tristani and Vestin (2004) employ macroeconomic variables to indirectly explain the risk premia. Their paper explains how macroeconomic factors (in‡ation, output gaps and
1Many papers provide evidence that the risk (term) premium in term structure of interest rate varies over time instead of being constant. Parts of this evidence consist of repeated rejec-tion of the expectarejec-tion hypothesis [Shiller, 1979; Startz, 1982; Shiller, Campbell and Schoen-holtz, 1983; Fama, 1984; Mankiw, 1986; Mankiw and Miron, 1986; Shiller, 1986; Campbell, 1987; Engel, Lilien and Robins, 1987; Fama and Bliss, 1987; Shiller and McCulloch, 1987; Hardouvelis, 1988; Froot, 1989; Simon, 1989; Campbell and Shiller, 1991 and others]
2Their two stage estimation methods is based on the asssumption that short term interest rates do not a¤ect macroeconomic variables.
the short term policy interest rates) drive movements in the term structure of interest rates and how they a¤ect the behavior of the risk premia embedded in observed yields. Their paper utilises a dynamic term structure model based on macroeconomic factors, which allows for an explicit feedback from the short term policy rates to macroeconomic outcomes. At the same time, the explicit modelling of risk premia captures dynamics of the entire term structures. They conclude that the dynamics of risk premia can ultimately be attributed to un-derlying macroeconomic dynamics3.
This paper can be divided into two main parts. In the …rst part, we generate measures of the risk premia of government securities for 43 countries over the period 1994-2006. In the latter part, we …nd the determinant of the risk premia using the data generated from the …st part. In examining the determinants of risk premia, we carefully deal with the characteristics of small sample sizes in our study. In the cross section regression analysis, we use the small sample version of the heteroskedasticity consistent covariance matrix estimates (HC3) suggested by MacKinnon and White (1985) to improve the performance of the analysis in small samples. In the dynamic panel regression, the determinants of risk premia are estimated using a Least Squares Dummy Variable Corrected (LSDVC) procedure proposed by Bruno (2005). This estimator is a recently proposed panel data technique that is suitable for small samples in unbalanced panels.
The result from the cross section analysis can be brie‡y summarised as follows. On average, over the period 1994-2006, the risk premia for holding gov-ernment assets required by risk averse investors is positively associated with the level of in‡ation and the budget de…cit as a percentage of GDP (both variables are signi…cant at the 1 percent level), and is negatively a¤ected by the country’s
3Anyhow, the paper did not include the foreign variables or exchange rate, which will provide fully satisfactory account of macroeconomic dynamics in the country of study e.g. Germany.
economic growth (signi…cant at the 5 percent level). Additionally, low income countries are estimated to have risk premia about 19 percent higher than in the high income countries outside the Eurozone, holding other variables constant. In the high income countries outside the Eurozone, the risk premia on holding government assets is predicted to be 10 percent more than those in Eurozone.
Using panel data analysis, we found that economic growth and the volatility of real e¤ective exchange rates are the main determinants of the risk premia in the full sample. Risk averse investors require lower risk premia for holding gov-ernment assets in countries with good economic performance i.e. high economic growth and a stable external price competitive position i.e. low volatility of real e¤ective exchange rate. If we split the sample by income group, economic growth remains the main determinant of the risk premia. However, we also …nd that the real e¤ective exchange rate plays an interesting and important role: in high income countries, devaluations bring favorable results to the economy as consistent with the Mundell-Fleming model. There is a better price competitive-ness which in turn reduces the country risk premia. The opposite relationship is found in the sample of low income countries. One possible mechanism explain-ing this may be that in …nancial vulnerable countries, weaker local currency can exacerbate the external debt service di¢culties. Devaluations therefore raise the country risk premia. This corresponds to the results from Cespedes, Chang and Velasco (2000).
The paper is organised as follows. The following section …rst outlines the de…nition of the risk premia and the departure from the existing literature. We then present a theoretical model for the ARCH-M methodology of time varying risk premia following Engle, Lilien and Robins (1987). Next, we construct mea-sures of the time varying risk premia for 43 countries over the period of 1994 to 2006. The results show that, in general, term premia exist, are time varying
and di¤erent between countries. After deriving measures of the term premia, we then ask what factors determine the movements in risk premia and what makes it vary across countries and through time4. Using cross sectional and panel data
regression analysis. Our main aim is to establish how macroeconomic, …nan-cial and political conditions determine the di¤erences in risk premia. The …nal section concludes.
2 Risk premia and related literatures
In this section, we …rst discuss the concept of the risk premia. We explain the rationale for estimating the risk premia from the term structure of interest rates. We also explain why the risk premia estimated here provides an alternative to those used in previous literatures. Lastly, we brie‡y discuss the rationale for using the ARCH-M model to estimate the risk premia.
The risk premium is the di¤erential in the expected rate of return on a risky asset as compared with a safe asset. The risk associated with holding government assets can be classi…ed into 2 aspects; the pure time factor of the risk, and the risk of default.
The pure time factor of risk refers to the term or maturity risk, and this is directly related to the term structure of interest rates in monetary economics through the expectation hypothesis. This hypothesis states that the interest rate on the long term asset must equal the average of the expected future interest rate on short term assets plus the term premium [Campbell and Schiller, 1991]. Hence, this term premium is simply an increment of return required to induce investors to longer term securities. The longer maturities entail greater risks for
4Assuming that investors form their expectations concerning movements in the interest rate using all available information, perfect capital mobility no longer implies that interest rates on the same asset class are equal across countries. The widely used measure of risk in …nance is the volatility, however, in an arbitrage free economy; the risk perceived corresponds to the relevant information available to an investor as well.
the investor. With longer maturities, more catastrophic events might occur that may impact the investment, hence the need for a risk (term) premium5. This
pure time factor of risk premia series can be directly estimated by the ARCH-M model by Engle et. al. (1987).
The risk of default refers to the likelihood of the loan not being repaid. Although it is generally recognised that securities issued by governments are relatively safer than other types of assets, the risk associated with holding them as perceived by international investors, varies according to the economic and political conditions of the country of issuer6. This risk is thus country speci…c
and is regarded as a country’s credit-risk.
Previous literature addressing cross country comparison of risk premia in-cludes Alesina, DeBroek, Prati and Tabellini , 1992; Lemmen and Goodheart , 1999; Giavannini and Piga, 1994; Favero, Giavazzi and Spaventa, 1996; IMF, 1997; Mc Cauley, 1996; Eij…nger, Huizinga and Lemmen, 1998 . However, these works examine risk premia based on the credit risk of government debt. I be-lieve that the measure of the risk premia in my study is a somewhat better measure of risk in holding government assets than the government defaulted risk constructed by previous literatures in several ways as follows.
Alesina et. al. (1992) study the default risk on government debt in OECD countries. The risk is derived by comparing the return from holding government debt with the return from holding corporate debt denominated in the same currency. However, the drawback is that the measure of default risk tends to be sensitive to signi…cant changes in private risk. Additionally, Alesina et. al.
5This explanation depends on the distant future being more uncertain than the near future, and risk of future adverse events (such as default and higher short-term interest rates) being higher than the chance of future positive events (such as lower short-term interest rates).
6This concept is quite similar to the asset market and portfolio balance approach in inter-national economics which states that domestic and foreign bonds are not perfect substitutes and foreign bonds carry some additional risk with respect to domestic bonds. However, in some countries with less …nancial stability, the domestic bonds may be relatively more risky than the government bonds in developed countries.
(1992) consider a variety of di¤erent maturities for both public and private yields. However, di¤erences in the maturity between the public and private yields may lead to inaccurate measurement of the magnitude of government default risk.
Lemmen and Goodheart (1999) …nd the determinants of credit risk in the European government bond markets using …xed e¤ects estimation. The risk speci…ed in their work is the default risk (credit risk) proxy by the spread of 10-year benchmark government bond yields over the corresponding swap yield of the same 10-year maturity denominated in the same currency. Although the risk speci…ed in Lemmen et. al. o¤er an improvement to the one used by Alesina et. al. (1992), the risk measure still has several problems. Firstly, the risk premia may not be a good proxy for country risk if the government private bonds interact with each other. According to Lemmen et. al. (1999), uncertainty about government debt servicing will a¤ect private sector risks par-ticularly when bank or other …nancial institutions hold large proportion of their assets in government debt, leading private and public risks to move in a lockstep fashion. Secondly, Lemmen et. al. consider government bond redemption yield data. The use of redemption yields introduces coupon reinvestment risks in the default risk measure. The redemption yield depends on the coupon size. To solve this problem, we use zero coupon yields data to calculate the risk premia. Other works employ the credit risk of sovereign debt, which can be assessed by comparing yields on domestic government bonds with high quality private risk represented by interest rate swap yields [Giavannini and Piga, 1994; Favero, Giavazzi and Spaventa, 1996; IMF, 1997; Mc Cauley, 1996; Eij…nger, Huizinga and Lemmen, 1998]. The risk premia measures in these literatures cannot dis-tinguish between credit risk and liquidity risk. The measure of the risk premia in these studies requires the assumption that variations in liquidity are
negli-gible. However, liquidity e¤ects may play a central role in government assets return. In my study, the liquidity e¤ect is automatically taken into account in the risk premia estimation.
3 Methodology: Measuring risk premia
This section describes the construction of our risk premia data. Section 3.1 describes the source of data for calculating the excess holding yield for 6 month treasury bills over 3 month treasury bills in 43 countries over the sample period of 1994:12 to 2006:2. Due to the limited availability of the zero coupon yield data, there are 43 countries in our studies. These include both developed and developing countries. See table 1.1 for a list of countries, data de…nition and the period of observation. Section 3.2 presents the theoretical derivation of the time varying risk premia. Section 4.1 uses the calculated excess holding return to generate the risk premia data by applying the ARCH-M methodology. The formulation closely follows Engle, Lilien and Robins (1987). The risk premia is the dependent variables in the cross section regression and the panel data analysis in sections 5 and 6, respectively.
3.1 The data
The term structure data available in each country start in di¤erent years and was collected from Bloomberg L.P. We use monthly observations of the yield on short term assets, i.e. 3 month- and 6-month treasury bills, to calculate the excess holding yield. We use the volatility of excess holding yield to generate the risk premia.
Instead of using the outstanding coupon treasury securities to calculate the excess holding yields, we use the calculated zero coupon instruments (…xed income) instead. This methodology is the same as Dotsey and Otrok (1995)
and Harris (2004)7. The zero coupon instruments make a single payment at the
maturity date. The size of the payment is the face value of the instruments. The advantage of the zero coupon bills is that it is free of liquidity and coupon e¤ects that are common in outstanding treasury securities. The data is, therefore, of the same type as that is analyzed in Campbell and Schiller (1991). This type of data is suitable for the analysis of term structure of interest rate since they have no e¤ects from di¤erent coupons and compounding methods. To interpret a zero coupon yield index, the zero coupon yields are derived by stripping the par coupon curve. For example, the USD Government Agency (FMC84) Zero Coupon Yield is the zero coupon rate derived by stripping FMC8 curve84. Most
of the yield indices are denominated in national currencies except Turkey, Brazil and Uruguay. These 3 countries are denominated in US Dollars. The dataset we obtained here is daily reported, and the last observation of each month is therefore chosen to serve as the end of month observation. Naturally, the 30th or 31st data of each month is used except for national Holidays or other non-trading days.
In estimating the term premia, we …rst de…ne the excess holding yield. The formula for constructing the excess holding yield of 6-month over 3-month zero coupon treasury bills is analogous to Engle, et. al. (1987), Dotsey et. al. (1995) and Harris (2004). To set the notation, yt6;3 is de…ned as the excess holding
return from holding a 6-month treasury bill compared to the return from holding consecutive 3-month treasury bills. Rt is the 6-month zero coupon treasury bill
rate and rt is the zero coupon yield of the treasury bill with maturity of 3
months. The excess holding period yield can therefore be calculated as:
7Engle, et. al. (1987) uses the treasury bills rate to calculate the riks premia. However, the US treasury bills are zero coupon bills in that they do not pay interest prior to maturity; instead they are sold at a discount of the par value to create a positive yield to maturity.
8FMC stands for Fair market value curve. The fair market value indices are derived from data points on Bloomberg’s option free market curves. The yield at each maturity point represents the composite yield of securities around that maturity.
y6t;3=h(1 +Rt)2=(1 +rt+1) i
¡(1 +rt); (1)
and following Engle et. al (1987), the linear approximation of equation (1) is used to calculate the excess holding yield as follow,
Prior to generating the risk premia, it is useful to brie‡y explain the de-scriptive statistics of the excess holding yield in the di¤erent countries. This will help in visualising the expected characteristics of risk premia.
Table 2.1 illustrates descriptive statistics of the excess holding yield gener-ated from equations (1). The standard deviation of the return measures the average deviations of the return series from its mean, and is often used as a measure of risk. A large standard deviation implies that there have been large swings in the return series of assets. The number of observations is represented by number of months observed. The main …ndings are summarised as follows.
Firstly, the mean of the excess holding yield for 6 months vs 3 months of our sample countries is positive in sign with value between 0 to 1 per cent per annum. Argentina and Uruguay are exceptions, the mean of the excess return is -3.95 and -0.99 percent per annum, respectively. This means that an investor would be better o¤ if he keeps investing in a shorter term asset (3-month bill) for a year than buying a single 6-month treasury bill which gives less return in time t+ 1: Additionally, the excess holding yield of government securities in these 2 countries is extremely volatile with standard deviations of 18.09 and 9.73 in Argentina and Uruguay9, respectively. The data available for Argentina
9The volatility of excess return is also increasing with maturity of longer term bonds.¡s:d:12;3> s:d:6;3¢:In table 2.2, the standard deviation of excess return in Argentina
and Uruguay are 48.96 and 35.15, respectively. The excess holding yield in these 2 countries are also the most volatile among 43 countries in this study.
is from 1998:07 to 2002:03. Hence, it includes the time of economic crisis in Argentina in 2001-2002. This entailed output falling by 20 percent over 3 years, high in‡ationary pressure, a severe devaluation of Argentine peso, government debt default, and lastly, a stagnant banking system. Over the period of study, the excess holding yield in Argentina hit its low at -71.716 per cent per annum in late 2001. This probably re‡ects the lack of con…dence in economic prospects as investors do not want to take a risk in longer term assets. From Figure 1.1, thanks to the currency board, we can see a period of stability in the excess holding yield from late 1998 to late 2000. The volatility coincides with the time of crisis1 0.
In 2003, Uruguay ( see Figure 1.41) went through a similar economic and …nancial crisis which developed mostly from external factors, not least the crisis in Argentina. The crisis started by the devaluation in Brazilian Reais in 1999 made Uruguayan exports relatively less competitive. In late 2000, the situa-tion was exacerbated by the economic crisis in Argentina, which is Uruguay’s ma jor trading partner. Subsequently in mid 2002 there was a bank run due to massive withdrawals from Uruguayan banks. The bank run was unfortunately overcame by massive borrowing from international …nancial institutions which in turn, led to a serious debt sustainability problem. Unsurprisingly, there was considerable volatility in the excess holding period return during late-2001 to mid-2002. Although Uruguay’s economy recovered in 2003 through improv-ing its export performance and a more positive investment climate, the excess holding yield swung wildly over the studied period. This re‡ects a persisting unstable …nancial system.
At the other extreme is the excess holding return of government securities in the Philippines which has a mean value of 1.91 percent per annum. It is also highly volatile with a standard deviation of 2.10. Figure 1.32 shows that
the excess holding yield ‡uctuates wildly throughout the period of study. The excess holding yield is especially volatile with the sharp spikes in 1997-1998 and in late 2000 owing probably to the Asian …nancial crisis and oil price shocks, respectively. On the other hand, the Philippines was less severely a¤ected by the Asian …nancial crisis of 1998 than its neighbors, aided in part by its high level of annual remittances from overseas workers, and no sustained run up in asset prices or foreign borrowing prior to the crisis. The impact from surging petroleum prices shock during late 2000 was more serious since the Philippines is an oil importer. Overall, we …nd that the excess rates of return from holding Philippines’ securities are highly erratics.
Apart from the countries already mentioned, there have also been large swings in the excess return series in Brazil, with a standard deviation of 4.27 (see table 2.1). This is probably because Brazil was also a¤ected by the South American economic crisis of 2002. Like other emerging market economies in general, Brazil was susceptible to contagion e¤ects. In Brazil’s case, it was contagion from Argentina’s economic melt down causing a crisis of con…dence among investors and lenders who were demanding higher interest rates. That put increasing pressure on the Brazilian economy to come up with those higher interest rates. Figure 1.5 shows that the excess holding yield series is again extremely volatile.
Our second …nding is that the average excess holding return is statistically not di¤erent from zero over the period of observation in all 43 countries. How-ever, we cannot yet conclude that the excess holding yield has a zero mean in the long run. This basically highlights the fact that there is a lot of noise. The high standard deviations distort the result and cause the mean to be statisti-cally equal to zero over the short sample period. The extreme examples are Argentina, Uruguay and Brazil as we have discussed.
Thirdly, the excess holding yield series which are less volatile relate to economies with stable …nancial systems and better economic development. For example, the mean of the excess return is relatively lower but exhibits much less variation over time in the majority of countries in the EU, compared to the rest of the world.
Additionally, among EU member countries, the excess return series of gov-ernment assets in Turkey, Poland, and Hungary are highly volatile with the standard deviation of 1.63, 1.48 and 1.40. The mean excess holding yield of these countries ranges from 0.02 to 0.46 percent annually.
Among countries in the Asia Paci…c region (excepting the Philippines), the average excess holding yield is between 0.11 to 0.59 percent per annum. The volatility of excess returns is not much higher than those in the EU countries, except in the Philippines and Hong Kong. The excess return in the Philippines is highly volatile with a standard deviation of 2.10, and mean return of 1.91 percent per annum.
Lastly, the excess return of 12-month over 3-month zero coupon rate is con-structed to test the robustness of the econometric results. y12t ;3is de…ned as the
excess holding period returns from holding 12-month treasury bills for 3 months compared to the return from holding 3-month treasury bills. The unit of time period int stands for every 3 months11. Following the same fashion as (1), the
excess holding yield of 12-month versus 3-month treasury bill can be generated as yt12;3 = " (1 +Rt)4 (1 +rt+3) (1 +rt+2) (1 +rt+1) # ¡(1 +rt); (2)
and the linear approximation is
Table 2.2 illustrates descriptive statistics of the excess holding yield gener-ated from equation (2). The results show that mean and volatility of excess return are increasing with maturity of longer term bonds. There is higher un-certainty associating with the longer horizon, thus investors require more excess return. The excess return series are also more ‡uctuate with longer maturity spread. In table 2.2, the standard deviation of excess return in Argentina and Uruguay are 48.96 and 35.15, respectively. The excess holding yield in these 2 countries are also the most volatile among 43 countries in this study.
The next section describes how the excess holding yield data can be used to construct risk premia.
3.2 The theoretical derivation of time varying risk premia
Engle, et. al. (1987) construct an ARCH-M model where the conditional vari-ance of excess return determines the current risk premium. They then test their model by applying it to quarterly data on 3-month comparing to 6-month US treasury bill rates from 1960:Q1 to 1984:Q2. The data are obtained from Salomon Brothers. The results shows that the risk premia vary systematically over time with agent’s perceptions of underlying uncertainty.
In this section we generate measures of the term premium by estimating the ARCH-M model of excess holding yields for 6 month treasury bills over 3 month treasury bills over the sample period of 1994:12 to 2006:2. The formulation closely follows Engle, et. al. (1987) and speci…es that the contemporaneous expected conditional standard deviation of the error term be included in the mean equation of the excess holding yield. This speci…cation follows from a micro-founded model with risk averse agents.
Firstly, the excess holding yield can be decomposed:
where(yt)is the excess holding yield on 6 month zero coupon treasury bills.
The non-stochastic term¹t is the risk premium or the expected return that the risk averse investor would demand for holding the (riskier) long-term asset. In contrast,"tis the di¤erence between the ex ante and ex post rate of return which
is unforecastable in an e¢cient market. This means that the expected excess return from holding the longer-term asset is just equal to the risk premium
The equation for risk premium is expressed as
¹t=¯+±ht; ± >0; (4)
where ht is the conditional standard deviation of the unforecastable shocks
("t) to the excess return on the long term asset. The term± is the coe¢cient of
relative risk aversion. The risk premium is assumed to be an increasing function of the conditional standard deviation of the unforecastable shocks ("t).
The conditional variance of the error term is h2
t and is a function of the
information set available to investors.
h2t =V ar("tjall available information) (5)
We note here that the model takes the mean as a linear function of the stan-dard deviation(ht)instead of the variance
. This represents the assumption that changes in the variance are re‡ected less than proportionally in the mean. This speci…cation has been widely used by other papers such as Domowitz and
Hakko (1985), and Bollerslev, Engle and Wooldridge (1988).
Following Engle, et. al. (1987), it is assumed that the conditional variance is a weighted sum of past squared innovations, "2
t¡i. This conditional variance
follows an ARCH(p) process as follows:
h2t =®0+®1 p X i=1
Here, the variance of the error term depends on the intercept®0 and the
weighted average of past squared innovations, where wi are the weighting
para-meters. Using monthly observations1 2, the ARCH speci…cation has 12 months
lags13 as we assume that information from the past year is useful for predicting
the mean. We discount the older information using a linearly declining weight scheme wherewi= (13¡i)=78, andi= 1¡12. This declining weight scheme on
lag structures also helps cope with the collinearity of the past square innovation terms,"2
t¡i [see Engle (1982)]. The equation can therefore be written as14
h2t =®0+®1 µ 12 78" 2 t¡1+ 11 78" 2 t¡2+::+ 1 78" 2 t¡12 ¶ : (7)
From the speci…cation above (equation (3)-(5)), we can conclude that the conditional mean of the excess holding yield E(yt)depends on the conditional
standard deviation of the unforecastable error term. Given that the variation of return measures riskiness, asEt¡1yt= ¹t;the risk premium is an increasing
function of the conditional standard deviation of the returns.
The model speci…cation above is used to generate risk premia for our entire sample.
1 2ELR use quarterly formulation and use four lags.
1 3The conditional variance follows a 12-order autoregressive process.
1 4We use monthly data and assume that the useful information for predicting the mean comes from the past year. Thus, in the conditional variance equation, we specify the declining weight on lag structure of past square innovations as in equation (7). However, Engle, Lilien, and Robins (1987) use quaterly data, the lag structure is instead characterised by h2
4 The variables
This section describes characteristics of the dependent variable, the risk premia and the explanatory variables.
4.1 Dependent variable: Risk premia
This section describes the risk premia data which is the dependent variable in the cross section regression and the panel data analysis sections. The risk premia generated from volatility of excess holding yield is referred to as the ex-post term premia or liquidity premia since the excess holding yield represents the realised or expost premium from holding the long-term as compared to short-term securities.
In this section, we present the estimation of the risk premia for 43 countries derived from the ARCH-M model. The estimated risk premia (together with the excess holding yield) are presented in …gures 1.1 to 1.43. This is to illustrate their characteristics over time and across countries. We …rst provide some descriptive statistics of the estimated risk premia.
Table 2.3 gives descriptive statistics of the risk premia of 6 month versus 3 month treasury bills across the sample period of 1994-2006. …gure 2.1 shows average risk premia over the period of 1994-2006 for all 43 countries. The table and …gures show that the risk premia is highest in the Philippines. The risk premia here are also highly volatile with standard deviation of 0.58, and with average risk premium of 1.98 percent annually.
In the Latin American countries, the risk premia are highly volatile with standard deviations between 0.52 (Mexico) to 1.94 (Uruguay). The risk premia is relatively low in almost all European countries and the series are much less volatile. Excluding the Czech Republic, the average risk premia in the EU ranges from 0.06 to 0.27 percent annually with standard deviations ranging from 0.10
to 0.23. Hence, there seems to be a relationship between economic as well as …nancial development and the risk premia.
Table 3.1 illustrates estimated coe¢cients and their t-statistics for each of the 43 countries. The notation of parameters corresponds to equations (3) and (4). The results from table 3.1 can be summarised as follows. Firstly, there is an ARCH in mean relationship in 16 out of the 43 countries. The ARCH in mean relationship exists when the disturbances are heteroscedastic and the standard deviation of each observations is found to a¤ect signi…cantly the mean of that observation (®16= 0and±6= 0). Additionally, the ARCH-M coe¢cient
shows the correct sign (± >0) in 34 out of the 41 countries; the risk premia is an increasing function of the conditional variance of returns15.
Secondly, from the result of ARCH-M estimation in table 3.1, the conditional variance of ARCH (12) process is constant(i.e. ®1 = 0and thus±= 0)in China,
Hungary, Indonesia, Korea, and Sri Lanka. The models show relatively ‡at and less volatile risk premia in Indonesia and Sri Lanka as are illustrated in …gures 1.19 and 1.26, respectively. However, this does not imply that the risk premia of government assets in these countries are constant.
From the plots of the excess holding yields and estimated risk premia, the series of excess holding yield in these …ve countries are so noisy16 that a
sys-tematic pattern of conditional heteroscedasticity does not hold given the quite short time-horizon under consideration. Thus, the conditional variance cannot be predicted by the past squared innovations as is suggested by Engle, et. al. (1987). We also …nd that the excess return series shows extreme volatility in
1 5We can conduct the sign test to see whether there is a signi…cant positive relationship between the risk premia and the conditional variance of return. The null hypothesis to be tested here is that there is no signi…cant positive relationship between them. This hypothesis implies that both the positive and negative of±in equation (4) are equally likely to be larger than the other. The results show zero p-value, which indicates that there is a strong positive relationship between the risk premia and the volatility [ Pr ( k>= 34) = 0.000013, Pr ( k
<= 34) = 0.999998, given N=41, k=34 ].
1 6There is no variation in volatility of the excess holding yield. In other words, the series are constantly highly-volatile.
Hungary (Figure 1.18) and Korea (Figure 1.25). The excess return swings wildly (with periods of both negative and positive excess return) without any system-atic pattern in Indonesia and Sri Lanka. We cannot …nd information for the risk premia in China (Figure 1.8) and Slovak Republic (Figure 1.36). Again, this can be attributes to the short horizon of the observations in China and Slovak Republic. (see table 1.1 for data appendix)
Lastly, for some countries, although the disturbance is heteroscedastic(®1 6= 0)
, the data are not suggestive of an ARCH-M process i.e. the conditional standard deviation does not a¤ect the mean. These countries are Norway, Sweden, Fin-land, Greece, IreFin-land, Turkey, South Africa, Argentina, Uruguay, Israel, Hong Kong and Hungary. From …gures, there is no period of stability in the excess holding yield in any of these countries. Hence, the estimated risk premium is characterised by a relatively ‡at line. Good examples here are the excess holding return series in Sweden, South Africa, Israel and Ireland. In Sweden, the variance of the excess return is very stable as illustrated in Figure 1.37. The excess return series in South Africa (see Figure 1.43) ‡uctuates around the constant mean with a brief shock in 1998. In Ireland, the excess return is also volatile throughout (see Figure 1.21). The excess return in Israel is severely volatile around the constant mean (see Figure 1.22), the series distributed evenly between positive and negative values. This re‡ects a fairly unstable …nancial condition in this country. The risk premia is unsurprisingly high throughout. The problem therefore is that the time period under consideration is not long enough to observe both periods of stability and volatility e.g. Engle, et. al. (1987) look at the risk premia in USA during 1960-1985, wherein there is a period of stability followed by a volatile period. In order to …nd an ARCH-M process, the samples must contain both.
and the past innovation does not contain information of the risk premia such as Turkey and Uruguay (see Figure 1.39 and 1.41). For Argentina (see Figure 1.1), there is too large shock in 2001 following period of stability, thus it mimics the predictive ability of the past innovations. Similarly, surrounded by periods of stability in excess holding yield, there is a large shock 1997-1998 in Hong Kong (see Figure 1.17) according to the Asian …nancial crisis.
In Finland, there is a negative time trend during late 20th century (see Figure 1.14). The mean and variance of the excess return are trending downward over the period of studies. On the other hand, there is no trend in the excess return in Greece and Norway, but the series is highly volatile that the risk premia is unpredictable.
As mentioned above, there is a signi…cant ARCH in mean relationship in 26 countries (®1>0 and± >0)in our study. The characteristics of the excess
return is quite similar to the case of the USA during 1960-1985. From Engle, et. al. (1987)’s work, over the period of analysis there are a few interesting shocks in the US economy. There was an oil price sho ck in 1973 and 1980, and the severe economic recessions in early 1982. During these periods, there was instability in …nancial and economic conditions, and people lost con…dence in the assets markets. They were unable to forecast future returns and demanded more return from holding long-term assets. The volatility in the excess holding yield produces a higher risk premium in these periods, However, during the more stable period (1960-1967), we …nd that the risk premium is quite low and the long run value of the excess return is constant. In our work, the excess returns of 6 month treasury bills in France (Figure 1.15), Mexico (Figure 1.27), Malaysia (Figure 1.28), New Zealand (Figure 1.31) follow the same pattern as the USA case in Engle, et. al. (1987): there is a period of tranquility followed by a period of volatility. Brazil (Figure 1.5) also follows this pattern, but the
volatility in the excess holding return is more drastic.
In Australia (Figure 1.2), Austria (Figure 1.3), Belgium (Figure 1.4), Czech Republic (Figure 1.10), the excess holding return is characterised by a negative time trend in short run (during late 20th century) and ‡uctuates around the constant mean in the long run. In Spain (Figure 1.13), the mean of excess return ‡uctuates up and down but the variances have large swing. There are time trends in the excess return and its variance is not constant throughout the period of studies with shocks in some periods in Germany (Figure 1.11), Switzerland (Figure 1.7), Canada (Figure 1.6), Colombia (Figure 1.9), Denmark (Figure 1.12), India (Figure 1.20).
Figures 1.1-1.4 illustrates the average risk premia for all 43 countries over the period of 1994-2006. Figure 2.1 is the average risk premia for holding 6 month treasury bills (comparing to 3-month treasury bills). Figure 2.2 is the average risk premia for holding 12 month treasury bills (comparing to 3-month treasury bills). The purpose of …gure 2.2 is to show that the di¤erence in average risk premia across countries is consistent across maturities. We …nd that the risk premia is generally low in countries with better …nancial development and economics conditions. Government assets in Singapore,Australia and Japan are relatively less risky compared to other countries in the study. Government assets in the Philippines and all Latin American countries are considered to be more risky than the rest. We can also perform country comparison of the risk premia by considering the countries’ income and economic development. Figure 3.1 presents risk premia (for holding 6 month treasury bills) comparisons by country group. We …nd that the risk premia of government assets in the non-OECD countries are relatively higher than the non-OECD country group. Figure 3.2 presents risk premia (for holding 6 month treasury bills) comparisons by country’s income. The higher income countries have relatively safer government
From a rough comparison of risk premia in 43 countries in this study. It is useful to extend an analysis by doing the cross section and panel data analy-sis. We examine whether the country’s macroeconomic variables a¤ect the risk premia in section 5 and 6.
4.2 Explanatory variables:
This section de…nes our control and explanatory variables used in the risk premia regression and discusses the expected sign of relationships with the risk premia. The macroeconomic variables we examine are economic growth (GGDP), the in‡ation rate (IN F L), the real e¤ective exchange rate(REE R), and the volatil-ity of real e¤ective exchange rate, (V RE ER). The government …scal variables pertain to government debt as a percentage of GDP(DE BT GDP) and the …s-cal de…cit as a percent of GDP(DE F GDP):The institutional variables consist of political constraints (P OLCON5)and a political risk index(IC RG):These variables will be de…ned subsequently. The sources and de…nition of data are detailed in the data appendix in table 1.2.
A preliminary examination of these relationships is presented by using the bar charts of the explanatory variables and bivariate regression plots of the risk premia and explanatory variables. The bar charts of average value of each explanatory variables are presented in …gures 4.1-4.9. The bivariate regression plots of the mean value of country’s risk premia and explanatory variables are presented in …gures 5.1-5.9.
The initial income level (GDP94) is our control variable for di¤erences in initial development levels. The initial level of income is derived from the natural log of real gross domestic product per capita in year 1994 of each country. Initial income also be a proxy for the …nancial development. We might expect that
there is less risk premia in holding government assets in countries with higher initial income and better …nancial development.
To control for heterogeneity among groups of economies, the regression analysis also include 3 groups of dummies, namely, E M U, N E M U_RIC H and P OOR. The dummy variable E M U stands for member countries of the European Monetary Union (EMU). We can refer to these countries as the Eu-rozone17. The second dummy variable,N EM U_RIC H stands for other high
income countries outside the Eurozone such as Denmark, Sweden, United King-dom1 8, USA, Canada, Japan, etc. Lastly, the dummy variable P OOR stands
for the low to middle income countries such as Czech Republic, Slovak Republic, Hungary, Poland1 9, Malaysia and Thailand, etc. The partitioning of these three
groups is presented in the variable list in table 2.1. The de…nition of high/low income countries is obtained from the World Bank (2006). Using dummy vari-ables also allow us to compare these 3 countries groups in the regression analysis. We discuss the reason for adding these three dummy variables in paragraphs below.
In our context, the inclusion of a Euro-zone dummy variable could be par-ticularly relevant. The in‡ation and exchange rate risk associated with their government assets are closely aligned, given their common currency. We begin our analysis in 1994 which is the second stage of the implementation of the European Economic and Monetary Union (EMU)20. At this stage, economic
1 7The Eurozone (also called Euro Area, Eurosystem or Euroland) is the subset of European Union member states which have adopted the euro, creating a currency union. The European Central Bank is responsible for the monetary policy within the eurozone.
1 8Denmark, Sweden and the UK are countries in the European Union that do not use the Euro.
1 9Czech republic, Slovak republic, Hungary and Poland joined the EMU on 1 May 2004. However, we do not include them in the group of Eurozone due to the ealrly stage of mem-bership and their income level.
2 0The …rst stage on the EMU (started on 1 July 1990) was to provide complete freedom for capital transactions, to improve economic convergence and to raise co-operation between central banks. There was also a free use of the European Currency Unit (a forerunner of the Euro currency). [European Central Bank, 2006]
convergence criteria among member countries had been in process, although the o¢cial launch of the euro was not until 1 January 1999. The EMU had a ma jor impact on the European …nancial markets and the management of the economic policies. It was argued that the currency risk would be reduced fol-lowing EMU. Government assets will instead be subjected just to the default risk.
"Government assets among EMU member countries would mainly di¤er with respect to their credit worthiness, liquidity and tax treat-ment since intra-EMU exchange risk should be zero and in‡ation risk would be the same for every country in the Euro zone" [Lemmen and Goodhart, 1999].
Thus the principal source of relative risk in government debt markets in EMU is credit risk. The variation in interest rates and exchange rates, which we regard as the market risk is no longer involved at least in intra-EMU [IBCA, 1996]. We thus may expect no signi…cant di¤erence between the exchange rate and in‡ation risk among EMU member countries in our regression21.
Basically, the initial income and these dummies are similarly functioning as control variables. They are employed to control for the …nancial develop-ment in general. The countries’ initial incomes take the economic covergence into account when we measure the economic growth. The dummy variables help enhance the predictability of the model by taking into account the income di¤er-ence and the in‡ation and exchange rate agreements22. An interesting research
to establish European Monetary Institute and to foster the process leading to the independence of the national central bank.
The last stage (1 Jan 1999) is to o¢cially introduce Euro, to conduct the single monetary policy by the Europena System of Central Banks and entry into e¤ect of the intra-EU exchange rate mechanism (ERM II)and into force of the Stability and Growth pact.
2 1We note that, however, the exchange rate risk still exists externally. The EMU member that trades externally has more risk than a member that does not i.e. it depends on extent of external trade.
question is to examine whether EMU member countries have lower risk premia as a result of their exchange rate arrangement. This issue will be unfolded in cross section and panel data analysis section.
Next, we discuss the characteristics of the explanatory variables. Countries with superior macroeconomic conditions, less exchange rate volatility, better …scal conditions and more reliable political conditions, are expected to have lower risk premia. The superior macroeconomic conditions are characterised by low in‡ation rate and high output growth. The government will have a good …scal condition if it has low debt and budget de…cit in proportion with the gross domestic product. The political conditions are relatively more reliable if there is less political risk in the country and more stable government policy.
The percentage increase in gross domestic product (GDP) during one year de…nes economic growth,GGDP. Economic growth is de…ned as
The GDP data are available on a quarterly basis. GGDPitis the rate of change
in the gross domestic product of country iat quarter tcomparing to the same quarter last year, t¡4. In the risk premia regression, we use the natural log of the average GDP growth of each particular country over 1994 to 2006 as an explanatory variable. We expect that a good economic performance comes along with stable …nancial market conditions. Alternatively slow economic growth might make the government asset in that country be more risky.
The GDP growth data suggests that there tends to be convergence across the economies in our sample. Figure 4.2 is bar chart of economic growth on average over 1994-2006. It suggests that lower income or developing countries (labelled byP OOR) experience signi…cantly higher growth rates than the higher
and 3.4B show that countries with high incomes tend to have lower risk premia. We partially control for income by using dummy variables,NEMU_RICHandP OOR.
income group (labelled byEM U andN E M U_RICH). Comparing this …gure with the bar chart of each country’s initial level of income measured by the gross domestic product in 1994 (…gure 4.1), it suggests that the less advanced economies with lower value of initial income (and initial capital) have higher growth rate of income (and capital).
In the bivariate regression in …gure 5.1, there is a strongly negative relation-ship between initial level of income(GDP94)and the risk premia as suggested earlier. On the other hand, the bivariate regression in …gure 5.2 show a strongly positive relationship between the risk premia and economic growth. This rela-tionship is somewhat contradict to our prior that the better economic growth leads to less risk premia required. Referring back to the chart of average risk premia over 1994-2006 (…gures 2.1 and 2.2), the estimated risk premia for the developing countries are quite high. However, during this period the more back-ward economies have higher economic growth rate than developed countries as suggested by the convergence. This shows the importance of including the initial level of income variable to control for other factors determining the risk premia apart from the economic growth.
In‡ation is also a potential determinant of risk premia. Investors protect themselves by requiring nominal interest rates that compensate them for ex-pected in‡ation as well as for the risk that the in‡ation deviates from their expectations. The higher prices rise, the lower will be the purchasing power of the principal and nominal interest payments correspondingly must be higher. Not only do investors want to be compensated for the in‡ation they expect, they also want to be compensated for the risk that in‡ation could increase during the term of their loan. In‡ation (IN F L) is de…ned as the percentage change of consumer price index over the corresponding period of previous year. In the cross section regression, we use the natural log of the mean in‡ation for each
country over 1994-2006. We expect a positive relationship between the in‡ation rate and the risk premia.
The data suggest that the attempt to stabilise in‡ation among member coun-tries in EMU seems to be successful. This can be seen in the charts of average country’s in‡ation over 1994-2006 in …gure 4.3. Within the Eurozone (exclud-ing Greece23), the country’s average in‡ation over the period varies between the
minimum value of 1.88 percent24 in France to maximum value of 4.89 percent
in Italy (excluding Greece, the mean in‡ation of this group is 2.83 percent). As mentioned earlier, the in‡ation levels of the Eurozone members tend not to be di¤erent from each others possibly due to the single currency convergence criteria. The higher income countries (both inside and outside Eurozone) have lower in‡ation rate than the lower income group. Comparing in‡ation level between countries in EM U andN EM U_RICH, the di¤erence between these 2 groups is not obvious25. However, there is slightly higher variation in in‡ation
rates in the latter group. The developing countries group (P OOR) has highest levels of in‡ation and the variation of in‡ation rates is quite substantial.
The scatter plots illustrating the relationship between risk premia and the in‡ation are presented in …gure 5.3. From the …gure, the EMU members are clustered around one another. The ma jority of countries in the P OORgroup are more dispersed in terms of both the risk premia and in‡ation. Overall, the …tted line shows a clear upward trend, which re‡ects a strongly positive relationship between the risk premia and the level of in‡ation. Thet statistics from the single regression in both …gures are signi…cant at the 1% level.
2 3The average in‡ation over 1994-2006 of Greece is 8.21 percents which is substaintially higher than the rest of countries in the Eurozone . This is partly because Greece if the last country that join this group. Greece was quali…ed as an EMU memeber state in 2000 and was admitted on 1 January 2001.
2 4In the cross section regression, we use the natural log of this value instead.
2 5Additionally, we …nd that the mean in‡ation in the UK, Denmark and Sweden are not very much di¤erent from the Eurozone (see …gure 4.5). This is reasonable. These three countries are reluctant the to join the Eurozone on political ground, it is not because these three countries have problem qualifying for membership.
The real e¤ective exchange rate(REE R)provides a measure of a country’s competitive position over time by taking the e¤ect of price movements into account26. Movements in real e¤ective exchange rates provide an indication of
the evolution of a country’s aggregate external price competitiveness since it measures the currency’s appreciation/depreciation against a weighted basket of foreign currencies and adjusts for relative prices between countries. The goods and services produced in particular country may not …nd buyers in both foreign and domestic markets if there is a fall in competitiveness. An improvement/fall in international price competitiveness a¤ects the country’s international trade position, national production, employment and income. We might expect that a rise in theRE ER(a fall in international competitiveness) results in an economic contraction as suggested in the Mundell-Fleming model. This in turn might be expected to be associated with a rise in the risk premia for holding government bonds in that country.
We also link real e¤ective exchange rate volatility (V REE R) to the risk premia of government treasury bills. We measure real exchange rate volatility as the natural log of the standard deviation of the real e¤ective exchange rate over 1994-2006. Using monthly data (t)of RE ER in country i, we de…ne the annual standard deviation of the real e¤ective exchange rate as
V RE ER=¾REE R i = " 1 T T X t=1 (RE ERit¡RE E Ri)2 # :
2 6To explain the concept of real e¤ective exchange rate, we …rst refer to the real exchange rate. The real exchange rate is the nominal exchange rate adjusted for relative prices between the countries under consideration. It is expressed as:
whereErealis the index of the real e¤ective exchange rate,Eis the nominal exchange rate
(foreign currency per unit of domestic currency) in index form,P is the index of the domestic price level, and P¤ is the index of the foreign price level. Instead of using a single foreign
currency, the real e¤ective exchange rate is concerned with what is happening to it against a basket of foreign currencies with whom the country trades.[Pilbeam, 1998, pp.13-16]
In this analysis, more volatile real e¤ective exchange rates implies more un-certainty in the country’s competitiveness position. Thus, we would expect a positive relationship between real e¤ective exchange rate volatility and the risk premium.
Di¤erences in the country’s competitive position, as measured by the real e¤ective exchange rate(RE ER), between the three countries groups is less clear-cut in the data. The charts of the country’s average real e¤ective exchange rate over 1994-2006 are presented in …gure 4.4. On the other hand, the exchange rate volatility(V REE R)over the period is generally higher in theP OORgroup than the higher income group (EM U andN EM U_RIC H). Additionally, the ma jority of countries in the EM U group have relatively lower exchange rate volatility than the rest. The charts of the real e¤ective exchange rate volatility are presented in …gure 4.5.
The plots of the relationship between the risk premia and the real e¤ective exchange rate are presented in …gure 5.4. The impact of the country’s compet-itive position on the risk premia on holding 6-month treasury bills is unclear. Figure 5.5 presents data for the relationship between the risk premia and the volatility of the real e¤ective exchange rate. There is a strongly negative rela-tionship between the risk premia and the volatility of the real e¤ective exchange rate which is consistent with our prior. Thetstatistics from the single regression is signi…cant at the 1% level.
Government debt as a percentage of gross domestic product can be consid-ered as a determinant of government default risk. The higher the existing debt stock to GDP ratios, the greater the debt service obligations and the lower the government’s capacity to borrow and roll over debt declines. This ultimately may result in an increase in the risk of default. We thus might expect a positive relationship between the risk premia and the government debt. The regression
uses the natural log of the mean government debt as a percentage of GDP over 1994-2006.
An increase in the …scal de…cit might impact the risk premium for two rea-sons. Firstly, …scal expansion may worsen future public debt and increase the probability of a debt crisis. Secondly, it a¤ects public trust and investors’ ex-pectations. The ability to control …scal de…cits reveals information about gov-ernment preferences, the importance of lobbies (which expect tax cuts or ex-penditure increases) and the degree of reform implementation (i.e. future public de…cits.). Hence, we might expect the risk premia is increasing with the gov-ernment budget de…cit. In the regression, we use the mean of the de…cit as a percentage of GDP for countryi over 1994-2006,DE F GDPi.
The data for government budget de…cit and debt as a percentage of GDP over 1994-2006 are presented in …gures 4.6 and 4.7. There is not much di¤erent across the groups. In …gure 4.6, the negative value represents the government budget de…cit. On average of 1994-2006, majority of sample countries have government budget de…cit. The exceptions are Ireland, New Zealand, Brazil, Hong Kong, Singapore, Thailand, and Slovak Republic, which have government budget surplus. Due to the high variation among samples, we normalize this variable by taking the natural log of(1 + 0:1¤DE F GDPi)in the regression.
A scatter plot of the risk premia and the government budget de…cit data is presented in …gure 5.6. There is no signi…cant relationship between these two variables but the sign of the predicted coe¢cient is correct. We suspect, however, that the budget de…cit does not strongly drive risk due to the existence of the outliers e.g. Norway, Sri Lanka, India, Philippines and Singapore. We will leave this issue until the next section.
Figure 5.7 contains data on the risk premia and government debt. The pre-dicted coe¢cient of government debts is not statistically signi…cant.
Surpris-ingly, the plots show negative relationship between government debts and the risk premia. It can be argued that government debts are not always bad. Debts re‡ect the demand for government assets by investors. The greater demand for them (given that there is no constraint on the supply side) may also mean that they are safer bet than private assets or foreign assets. For example, Belgium and Philippines both have high government debt but the risk premia for holding securities in the former is less than the latter country. On the other hand, there are low government debts in Australia and Colombia. Unsurprisingly, the risk premia in Australia is lower.
The political variables used in this paper are the political risk index created by the PRS group and the political constraints index (P OLCON5) by Henisz (2002). The political risk index (ICRG) measures the political stability of countries on a comparable basis. The index is based on 100 points. The higher number of points indicates lower potential political risk e.g. 80-100 points rep-resent very low risk and 0-49.5 points reprep-resent very high risk. In the political risk assessment, the number of points depends on the …xed weight of the po-litical risk components. The popo-litical risk components and their weights in the parentheses are Government stability (12), Socioeconomic Conditions (12), In-vestment Pro…le (12), Internal Con‡ict (12), External Con‡ict (12), Corruption (6), Military in Policies (12), Religion in Policies (6), Law and Order (6), Ethnic Tensions (6), Democratic Accountability (6) and Bureaucracy Quality (4). The data forICRGare available annually. In the regression, we take natural logs of the mean of the political risk index over 1994-2006. We might expect a negative relationship between ICRGandRP3_6. In other words, lower risk premia for
holding government assets should be positively related to the ICRG rating. P OLC ON5measures the e¤ective political restrictions on executive behav-ior. It accounts for the veto powers of the executive whether or not there are,
two legislative chambers, sub national entities and an independent judiciary. The index ranges from zero to one, where the higher value indicates stronger political constraints on the government. We take the natural log of the average values ofP OLCON5over 1994-2006. The stronger political constraint re‡ects a more stable government policy, which may in turn result in reduced risk premia. Higher income countries tend to have lower political risk ratings (higher score) and stronger political constraints than the lower income group, as shown in …gure 4.8 and 4.9. From the scatter plots in …gures 5.8 and 5.9, the risk premia exhibit negative correlations with both political variables as expected. The scatter plot of the risk premia and the political risk rating is presented in …gure 5.8. The political risk index negatively determines the risk premia as we expected. The predicted coe¢cient is highly signi…cant (at the 1% level). The scatter plot of the risk premia and the political constraint is illustrated in …gure 5.9. The determinant of the political constraint index on the risk premia is less strong but the sign of the predicted coe¢cient is correct. The predicted coe¢cient is signi…cant at the 12% level.
The next section is to present the result from the cross section regression analysis.
5 The cross section regression
This section examines the determinants of risk premia on holding 6-month trea-sury bills in 43 countries using cross section regression analysis. We test whether macroeconomic variables, government …scal variables and political variables de-termine the risk premia. The dependent variable in the regression is the average risk premia for holding 6-month treasury bills comparing to 3 month treasury bills (RP3_6) for di¤erent countries over the period 1994-2006 (as depicted in …gure 2.1). In general, investors who hold these assets are mainly …nancial
institutions. These …nancial institutions are assumed to minimize investment risks by spreading assets among di¤erent investments both nationally and inter-nationally. The di¤erence between these 2 assets is that holding shorter term treasury bills is less subjected to liquidity risk. In other words, the ability to sell or convert a security into cash is obviously greater for the shorter term treasury bills.
A small sample version of heteroskedasticity consistent covariance matrix estimator, HC3 proposed by MacKinnon and White (1985)2 7 is applied to
cor-rect for heteroskedasticity in the cross-sectional data analysis28. The following
subsection are the results of the risk premia cross-section regression on the macroeconomic and political variables.
We …rst examine the correlations between risk premia and the explanatory variables across countries. The results are given in table 4.2. To set the nota-tion, ½ is the correlation coe¢cient. We notice that the risk premia is highly correlated with the political risk index (½=¡0:63), the political constraint in-dex(½=¡0:58) and in‡ation(½= 0:57):Other variables that are fairly corre-lated with the risk premia are real exchange rate volatility(½= 0:50), economic growth29(½= 0:43)and the budget de…cit as a percentage of GDP(½=¡0:17).
With the exception of economic growth, the signs of all the correlation coef-…cients are consistent with our priors corresponding to the previous section. Knowing that these variables are associated with the risk premia, we might
pre-2 7Long and Ervin (2000) produced an extensive study of small sample behaviour and arrive at the conslusion that HC3 provides the best performance in small samples (less than 250 observations) as it gives less weight to in‡uential observaitons.
2 8When the variance of the errors varies across observaitons, OLS becomes ine¢cient and the estimates of the standard errors are inconsistent. This result in incorrect inferences. For a careful data analysis, we thus correct for heteroskedasticity in the cross sectional data analysis by using MacKinnon and White (1985)’s HC3.
2 9Both In‡ation and economic growth are consirably correlate to the risk premia. How-ever, the correlation between these two explanatory variables is quite high:In order to avoid endogeneity problem, we should include both variabls in our equation. We can …nd the de-terminant of one explanatory variable on risk premia while controlling the impact of another explanatory variable.
dict that these variables would be statistically signi…cant predictor variables in the regression model.
The starting point for the risk premia cross-section regression3 0 is to regress
the risk premia on the macroeconomic variables, initial level of income and the country’s economic and income group dummies. The results are presented in column (1) of table 5. The results show that in‡ation(IN F L)and the economic growth (GGDP)are signi…cant at the 5% level31. The budget De…cit as a
per-centage of GDP(DE F GDP)has predictive power at the 10% level. Initial level of income is signi…cant at the 15 percent level. Central government debt as a percentage of GDP(DE BT GDP)and the real e¤ective exchange rate volatility
(V RE E R)do not statistically determine the risk premia. Approximately 74% of the variability of the risk premia is accounted for by the explanatory variables in the model.
Column (2) adds the political variables, P OLCON5 and IC RG to the model. The economic factors are robust to the inclusion of additional explana-tory variables. However, the economic factors highly dominate in the risk premia regression, thus the political variables have limited explanatory power32. The
sign of the predicted coe¢cients are as expected although are not signi…cant. We can conclude from the regression in column (2) that the short run macro-economic circumstances do most of the work in explaining the risk premia e.g. the higher in‡ation, the lower growth and government de…cit lead to lower risk premia. In contrast, the level of long run development as illustrated by the institutional variables, i.e. the political risk index and the political constraint
3 0The regression is based on the heteroscedasticity consistent covariance matrix (HCMM) version HC3 by Mackinnon and White 1985. This helps corerect heteroscedasticity in the small sample size model(n·250).
3 1The magnitude will be presented in the preferred model. It will be discussed in the latter paragraphs.
3 2Adding political variablesP OLCON5and ICRGseperately into the model in column (1) of table 5 also does not improve the explanatory power of each political variable in the regression.
index, and the public debt do not determine the risk premia. A good example is Belgium. The average government debt as a percentage of gross domestic prod-uct over 1994-2006 is high in this country (as illustrated in …gure 4.7). However, the risk premia for holding government asset is quite low (see …gure 5.7). For the case of this country, high debt may be a sign that a country is a safe bet.
Column (3) excludes the insigni…cant explanatory variables. The results from the previous section are unchanged. The e¤ect of the de…cit as a percentage of GDP,DEF GDP become stronger and is signi…cant at 5% level. The variables economic growth (GGDP)and in‡ation (IN F L)are once again signi…cant at the 5% level.33. The standardized coe¢cient (beta value) of this model is also
presented in table 5. It indicates the size of the change in the risk premia,RP36
(in term of its standard deviation) with respect to a one standard deviation in the explanatory variable. For example, based on the estimates in column (5), a one standard deviation increase in IN F L(from Germany to Portugal’s level) raises the risk premium by 1.29 of a standard deviation (from Germany to Indonesia’s level34).
Finally, it is possible that this outlying observations might skew our test for heteroscedasticity in column (3). We thus identify outliers or in‡uential obser-vations3 5. The outliers measure suggests removing observations in Argentina36,
Brazil, Norway, Sri Lanka, Indonesia, Philippines and Singapore. We omit these 7 countries from regressio